SOLUTION: The working day in a factory is 8 hours long. To cut the workforce by x% without affecting the daily production output, the management had to raise the working hours to 10 hours pe

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Question 894360: The working day in a factory is 8 hours long. To cut the workforce by x% without affecting the daily production output, the management had to raise the working hours to 10 hours per day. Find x.
The key has 20% as the answer. I don't understand how they got that answer.
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
( hours worked / day ) x ( workforce ) = daily production
Let +P+ = the daily production
The size of the workforce isn't given, so
I'll call it +100+
Before cutting workforce:
(1) +8%2A100+=+P+
After cutting workforce:
(2) +10%2A%28+100+-+100%2A%28+x%2F100+%29+%29+=+P+
-----------------------------------
(1) +P+=+800+
(2) +10%2A%28+100+-+x+%29+=+P+
(2) +P+=+1000+-+10x+
Substitute (1) into (2)
(2) +800+=+1000+-+10x+
(2) +10x+=+1000+-+800+
(2) +10x+=+200+
(2) +x+=+20+
x% = 20%


Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Lets say there are 100 workers working 8 hours a day
8*100 is 800 man work hours
if the number x works 10 hours for the same total of man work hours then 800/10=80 men working 10 hours
100-80=20 men cut
20/100=20% reduction
You now are using 4/5 or 80% of the work force. You are using 1/5 or 20% less.